I have been assured by a number of people that it is going to be a hard winter because the squirrels have been exceptionally active hoarding nuts. I want to believe this kind of observation because I want to tap into a knowledge that transcends and subverts the stultifying logic of measurement and science. I suppose the antithesis of this are the council goons that order chestnut trees to be cut down in case a conker falls on a passer-by or someone slips on a leaf.

A fully grown horse chestnut, Aesculus hippocastanum, will be more than 35m tall and almost as broad, and is unquestionably one of the finest flowering trees in the northern hemisphere. It is also one of those grown-up things that anybody in their right mind should celebrate, although conkers belong to children. I would love a conker to fall and hit me. Our own horse chestnut has not produced any fruit yet, but it is just six years old and they only start to flower around their seventh year. The flowers, balanced like pyramids of ice cream or white candyfloss, are at their best in early May, but the sticky buds break into glowing leaf in early April and the whole tree is a delight all spring and early summer. And in the hot, dog days of high summer, no tree casts such a congenial shade.

The conkers are the seed, with their pale hilum scar. The name comes from a dialectic word for snail shells, which were used for the game before the horse chestnut came on the public scene in the early 19th century. Before that they were the province of the private park, where all gathering of nuts, fruit or wild animals was considered poaching and punished with incredible harshness. So conker trees in public places represent a liberation of nature and public playfulness as well as decoration. It makes the action of the health and safety brigade doubly shameful.

Nothing has a sheen like a freshly exposed conker, and not many seeds are as beautiful as objects in themselves. I have just remembered that my twin sister and I used to make 'beer' by soaking handfuls of the empty seed shells or casings, which made a thoroughly satisfying froth and stained the water brown, which could then be poured into jugs. It had a sharp, slightly sour smell that was every bit as enticing as any proper beer has been to me since. In fact, the flower buds were occasionally used as a substitute for hops for making beer. In the second world war, conkers were roasted and ground to make a coffee substitute. By all accounts it was almost as disgusting as some of the insipid liquid that is often passed off as coffee by the various chains.

Horse chestnuts will grow fast and in just about any soil, reaching a great age. The oldest-dated trees in Britain are 400 years old now. They have been a completely friendly tree since they were introduced to this country in the early 17th century. They have no woodland or even rural association beyond a mannered parkland setting. Bushey Park has a superb avenue of them, planted by Christopher Wren in 1699, leading up to Hampton Court Palace. The Victorians loved them and you will often see them in parkland planted with similar huge exotics, such as with wellingtonias, copper beeches and London planes. For all their huge size, these are trees of domesticity. They are grown entirely for ornament, whereas almost all our native trees and quite a few introductions have had a range of essential uses throughout history. The timber of horse chestnut is soft and very white. It was apparently used for dairy maids' buckets because, if kept wet, it is slow to rot. But the demand for dairy maids' buckets has never warranted plantations of the trees even in the milkiest of times.

The red horse chestnut, A x carnea, is a cross with the red buckeye, A pavia, which is a very much smaller tree from North America, has rather dirty pink flowers which seem to me a pointless reduction of the incredibly beautiful white inflorescences of the original. It is smaller, rarely getting above 20m - which, I suspect, is why you quite often see it as a street tree.

A flava, or the yellow buckeye, has yellow flowers that open rather later and does best with some shelter until well established. There is also a cut-leaf job and a number of smaller trees, such as the sunrise chestnut (A x neglecta 'Erythroblastos') that read well on the page, but I confess I have never noticed them. The point is that the conker tree does it all.

The sweet chestnut, Castanea sativa, is a southern European tree and was almost certainly introduced by the Romans. It is happiest on well-drained or sandy acidic loams, so whereas the horse chestnut occurs everywhere, its sweet counterpart tends to be very localised. The casing of the nuts is as prickly as hedgehogs and they decorate the autumnal tree like limegreen Christmas baubles. The nuts are famously delicious but, unlike most nuts, they are relatively low in protein and fat but high in starch, so are traditionally used in chestnut-growing areas like the Pyrenees as a kind of flour to make bread and porridge. They need some warmth to mature, but perhaps one of the side benefits of climate change will be that we get a bigger and tastier chestnut harvest right across the UK.

The wood is fast-growing, hard and extremely long-lasting in the soil - ideal for fencing. The reason for this durability is that it forms a hardwood heart at a very early age and it is this that makes it able to cleave very cleanly and straight. I once bought 100 8ft chestnut stakes, each about 8in in diameter, and split them all into quadrants to use as the uprights for a woven hazel fence. Almost without exception this could be done cleanly using an axe and wedge. It was, slightly weirdly I confess, one of the most satisfying couple of hours of my life. Its ability to split into thin, strong posts make it ideal for paling or movable fencing that can be rolled up and quickly erected by the mile, yet remains almost as strong as oak. A thicker version of this chestnut paling was used in the Second World War to make over 1,500 miles of tank tracks on the Normandy beaches. Until 1900, all hops were grown up poles, each about 14ft tall and only about 1in in diameter at the tip. Each hop vine needed two poles, so around 2,000 were used for every acre of hops. This was serviced in Kent in particular (Herefordshire hops tended to grow up poles of coppiced ash) by coppices of sweet chestnut cut on a 10-year rotation. It is one of the best coppice trees, throwing up a mass of straight shoots with glossy saw-toothed leaves that have a remarkably exotic, almost tropical appearance.

This willingness to coppice can be used in the garden to make the tree into a multi-stemmed shrub, although if you have the space it makes a famously long-lived tree with close-ridged bark that often spirals around the trunk. The oldest surviving tree is reckoned to be between 3-4,000 years old and Sicily in particular has groves of very ancient trees. In this country there are numerous chestnuts that are medieval in origin although still callow in chestnut years, and if they are left to grow free from any council official fearful of branches falling on a litigious passerby, there is no reason to suppose they will not grow on for another thousand years yet.